In Washington, the policy debate around Medicare reform revolves around two options: the approach embodied by Obamacare, in which government adds a rationing system onto the traditional Medicare program; and the approach advocated by Mitt Romney and others, in which seniors choose between traditional Medicare and a set of new, privately sponsored health plans. But there’s another question worth asking: could private insurers play a role in improving the traditional Medicare program?

When we speak about Medicare’s problems, we usually talk about how much the program costs. Medicare is, along with the other government-run health care programs, the biggest driver of the federal deficit. But Medicare also is a big driver of the inefficiencies in our health care system: wasteful spending, inappropriate procedures, and outright fraud.

In theory, traditional Medicare has a lot of power to keep prices low, because Medicare’s size and market power mean that very few doctors and hospitals can afford to say “no” when Medicare demands lower rates. But Medicare doesn’t use this monopsony power to the degree that it could, leading to a lot of waste and inefficiency.

For example, under current law, Medicare must pay for health care delivered by any hospital or doctor willing to do so at Medicare’s rates—what wonks call Medicare’s “any willing provider” provision. In one sense, this is a good thing, because it limits the government’s power to distort the market. But if every provider can participate in Medicare, the program has limited leverage to steer seniors to the most cost-efficient providers.

For all the hype about “accountable care organizations,” which create hulking provider superpowers that purport to integrate care for their patients, there are a lot of reasons to be concerned that ACOs will use their market power to drive up prices, rather than deliver better care.

One of the big advantages of the privately-administered forms of Medicare, such as Medicare Advantage, is that they can negotiate amongst providers and do more to manage complex cases. That’s a big part of the reason that Medicare Advantage can offer a superior benefit package, compared to traditional Medicare. A recent study by three Harvard economists found that, using comparable benefit packages, Medicare Advantage was 9 percent more cost-efficient than traditional Medicare.

There are other things that private insurers do that Medicare does less well. Insurance companies have learned how to engage in proactive risk management for patients with chronic diseases, like diabetes, in order to ensure that patients avoid dangerous complications. In other words, private insurers can deliver higher quality care, along with keeping an eye on waste and fraud.

The trend toward higher-quality private insurance may continue within Medicare. Medicare Advantage continues to gain market share over traditional Medicare, despite looming Obamacare-related cuts to the program. If Republicans sweep into power in November, they will hope to enact the Medicare reforms advocated by Mitt Romney and Paul Ryan, which will bring more private options into the Medicare program.

But perhaps there’s a way to use the private sector experience to make improvements to the traditional, 1965-vintage Medicare program. One such approach would be to learn from the way insurers help administer health-care claims for large companies who “self-insure” their workers.

Under Section 514 of the Employee Retirement Income Security Act of 1974, or ERISA, companies who directly fund their workers’ health benefits, instead of purchasing health insurance on their behalf, are not bound by state insurance regulations. Because state insurance regulations often act to drive up the cost of health insurance, many companies—especially large ones with a broad risk pool—are better off if they self-insure their workers.

Typically, these large companies will outsource the administrative function of these self-insured plans to what are called administrative services organizations or ASOs. ASOs, which are often run by actual health insurers, also tend to be much cheaper than conventional insurance.

Unlike conventional insurance, where the insurer collects premiums and pays for health expenses, taking on the financial risk thereof, in the ASO model it’s the employer that takes on the financial risk for paying health expenses. The ASO administrator creates the co-pay system, the network of doctors and hospitals, reimbursement rates, etc. The idea is that insurers have broader expertise to manage health claims more efficiently than do individual companies, whose expertise lays elsewhere.

A Medicare ASO program could serve as a kind of bridge between traditional Medicare and Medicare Advantage. The ASO would apply the administrative services model to traditional Medicare, in which private insurers would process Medicare’s health claims, in the way that insurers do for companies that self-insure their workers.

The ASO could use Medicare’s conventional reimbursement rates, or use their own, either higher or lower rates, by negotiating directly with providers. An ASO program could include financial benchmarks, so that administrators are rewarded for saving Medicare money, or by increasing the quality of care.

The question, then, becomes where a Medicare ASO would fit into the national debate about Medicare reform. The original Paul Ryan idea, as mapped out in the first version of the Path to Prosperity, was that everyone under 55 would migrate over to a new system in which seniors were given a defined amount of money, which they could then use to choose from a menu of privately-run, government-approved health plans. In Ryan’s latest iteration, one backed by Democratic Sen. Ron Wyden (Ore.) and Mitt Romney, seniors would choose between these privately-run plans and the traditional government-run Medicare program.

Adding yet another form of Medicare to the mix may be too much to ask of Capitol Hill. The majority of Democrats are ideologically opposed to increasing the role of private insurers in Medicare, and indeed want to move in the other direction. Nearly every Republican, by contrast, has already voted to support the Ryan budget, which goes further in the direction of privatization than a Medicare ASO would.

It could be, however, be that a Medicare ASO could be added to the menu of plans offered under a Romney/Ryan-like competitive bidding system. The irony is an ASO is just the sort of thing that could help traditional Medicare succeed against private plans.

It’s all speculation for now, because we don’t know what the policy possibilities will look like after November. But the tens of millions of retirees who rely on the traditional Medicare program today could benefit from higher-quality care, at lower cost. We owe it to ourselves to think through the possibilities.